The system of linear equations has a unique solution. Find the solution using Ga

Algebra
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The system of linear equations has a unique solution. Find the solution using Gaussian elimination or Gauss-Jordan elimination.

 
x1 + 2x2 − x3 = 3
2x1 − x3 = −2
3x1 + 5x2 + 2x3 = 7
(x1x2x3) = 
 
 
Jul 17th, 2015

Thank you for the opportunity to help you with your question!

For better reading, x1 = x, x2 = y, x3 = z

(2) - (1) ====>  x - 2y = -5   ===>  x = -5 + 2y

(1) + (2) + (3)  ====>  6x + 7y = 8 

Plug x = -5 + 2y

6 (-5 + 2y) + 7y = 8

-30 + 12y + 7y = 8

19 y = 38

y = 2

x = -5 + 2(2) = -5 + 4 = -1


From (2)

2x - z =-2

2 (-1) - z = -2

z = 0


Therefore x1 = -1, z2 = 2, x3 = 0


Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 17th, 2015

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